We present searches for the leptonic decays B+ -> l+ nu and the lepton flavor violating decays B0 -> l+ tau-, where l=e,mu, with data collected by the BaBar experiment at SLAC. This search demonstrates a novel technique in which we fully reconstruct the accompanying Bbar in Upsilon(4S)->BBbar events, and look for a monoenergetic lepton from the signal B decay. The signal yield is extracted from a fit to the signal lepton candidate momentum distribution in the signal B rest frame. Using a data sample of approximately 378 million BBbar pairs (342fb-1), we find no evidence of signal in any of the decay modes. Branching fraction upper limits of B(B+ -> e+ nu)<5.2x10^-6, B(B+ -> mu+ nu)<5.6x10^-6, B(B0 -> e+ tau-)<2.8x10^-5 and B(B0 -> mu+ tau-)<2.2x10^-5, are obtained at 90% confidence level. Show Partial Abstract